Remove Abs from Norms of Vectors

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I have the following norm



Norm[a, b*c] // Sqrt[Abs[a]^2 + Abs[b c]^2]


How do I remove the Abs from it? 



FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0]


only kills the first Abs



Sqrt[a^2 + Abs[b c]^2]





list-manipulation simplifying-expressions vector







share|improve this question

























    up vote
    3
    down vote

    favorite












    I have the following norm



    Norm[a, b*c] // Sqrt[Abs[a]^2 + Abs[b c]^2]


    How do I remove the Abs from it? 



    FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0]


    only kills the first Abs



    Sqrt[a^2 + Abs[b c]^2]





    list-manipulation simplifying-expressions vector







    share|improve this question























      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      I have the following norm



      Norm[a, b*c] // Sqrt[Abs[a]^2 + Abs[b c]^2]


      How do I remove the Abs from it? 



      FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0]


      only kills the first Abs



      Sqrt[a^2 + Abs[b c]^2]





      list-manipulation simplifying-expressions vector







      share|improve this question













      I have the following norm



      Norm[a, b*c] // Sqrt[Abs[a]^2 + Abs[b c]^2]


      How do I remove the Abs from it? 



      FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0]


      only kills the first Abs



      Sqrt[a^2 + Abs[b c]^2]





      list-manipulation simplifying-expressions vector




      list-manipulation simplifying-expressions vector






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 51 mins ago









      chr

      232




      232




















          2 Answers
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          up vote
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          ComplexExpand@Norm@a, b c



          Sqrt[a^2 + b^2 c^2]







          share|improve this answer




















          • Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
            – chr
            33 mins ago










          • ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
            – That Gravity Guy
            18 mins ago


















          up vote
          1
          down vote













          If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to make expressions with Abs more costly:



          FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0, 
           ComplexityFunction -> (100 Count[#, _Abs, 0, Infinity] + LeafCount[#] &)]



           Sqrt[a^2 + b^2 c^2]







          share|improve this answer




















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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote



            accepted










            ComplexExpand@Norm@a, b c



            Sqrt[a^2 + b^2 c^2]







            share|improve this answer




















            • Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
              – chr
              33 mins ago










            • ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
              – That Gravity Guy
              18 mins ago















            up vote
            1
            down vote



            accepted










            ComplexExpand@Norm@a, b c



            Sqrt[a^2 + b^2 c^2]







            share|improve this answer




















            • Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
              – chr
              33 mins ago










            • ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
              – That Gravity Guy
              18 mins ago













            up vote
            1
            down vote



            accepted







            up vote
            1
            down vote



            accepted






            ComplexExpand@Norm@a, b c



            Sqrt[a^2 + b^2 c^2]







            share|improve this answer












            ComplexExpand@Norm@a, b c



            Sqrt[a^2 + b^2 c^2]








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 38 mins ago









            That Gravity Guy

            698410




            698410











            • Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
              – chr
              33 mins ago










            • ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
              – That Gravity Guy
              18 mins ago

















            • Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
              – chr
              33 mins ago










            • ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
              – That Gravity Guy
              18 mins ago
















            Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
            – chr
            33 mins ago




            Thx. Can you explain why ComplexEpxpand does it and Assumptions does not?
            – chr
            33 mins ago












            ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
            – That Gravity Guy
            18 mins ago





            ComplexExpand automatically assumes all its variables to be real. Other than that, I believe it's just a matter of behind-the-scenes expression manipulation (i.e. I don't know...). Though this idea reminds me of this post talking about different ways of assuming things (granted in relation to Integrate).
            – That Gravity Guy
            18 mins ago











            up vote
            1
            down vote













            If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to make expressions with Abs more costly:



            FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0, 
             ComplexityFunction -> (100 Count[#, _Abs, 0, Infinity] + LeafCount[#] &)]



             Sqrt[a^2 + b^2 c^2]







            share|improve this answer
























              up vote
              1
              down vote













              If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to make expressions with Abs more costly:



              FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0, 
               ComplexityFunction -> (100 Count[#, _Abs, 0, Infinity] + LeafCount[#] &)]



               Sqrt[a^2 + b^2 c^2]







              share|improve this answer






















                up vote
                1
                down vote










                up vote
                1
                down vote









                If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to make expressions with Abs more costly:



                FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0, 
                 ComplexityFunction -> (100 Count[#, _Abs, 0, Infinity] + LeafCount[#] &)]



                 Sqrt[a^2 + b^2 c^2]







                share|improve this answer












                If you have to use FullSimplify or Simplify, you can use the option ComplexityFunction to make expressions with Abs more costly:



                FullSimplify[Norm[a, b*c], Assumptions -> a > 0, b > 0, c > 0, 
                 ComplexityFunction -> (100 Count[#, _Abs, 0, Infinity] + LeafCount[#] &)]



                 Sqrt[a^2 + b^2 c^2]








                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 34 mins ago









                kglr

                161k8185384




                161k8185384



























                     

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